Strollers but not chain places Midtown East?

Looking for new places to take our newborn to for dinner (not for her to eat of course but places that have room for strollers). Do most people just call restaurants ahead to see if they can accommodate a stroller? I know places like California Pizza Kitchen, Outback Steakhouse and most diners accommodate, but I'm looking for places that are still fairly casual but a bit better cuisine.

Ali Baba is on 34th St., b/t 2nd and 3rd Av. Very good Turkish food and friendly service. When we were there for dinner a few months ago, we were seated in the back area. There was a couple at one of the tables with a baby though I'm hazy as to whether they had a stroller with them. I think there is room for one back there, but it would be best to call and check. They are also open for lunch and brunch.

Cibo, on the corner of 2nd Av. & 41st St., is a family-friendly neighborhood restaurant with very good Tuscan/New American cuisine. It's a fairly large place, i.e., two dining rooms and a separate bar room, plus nicely-spaced tables, so a stoller can be accommodated.

While Ali Baba is child-friendly, there is not much room for a stroller. They have high chairs, but since the OP's child is newborn, that's not really an option right now. I would suggest bringing her in the infant car seat, and leaving the stroller base at the front and resting the car seat on a chair at the table. Also, go early.

We took our ten month old to Tarabia on 1st avenue and they could not have been nicer. It's a small restaurant, but we went for lunch on a saturday so it wasn't too crowded. It's Turkish food - and quite good. But the staff was so sweet to our messy baby!